Chapter: Basic Electrical and electronics - Digital Electronics

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Boolean Algebra

Verification Of De Morgan's Theorems: De Morgan's First Theorem states: De Morgan's Second Theorem states:

BOOLEAN ALGEBRA

 

Boolean algebra is an algebraic structure defined by a set of elements, B, together with two binary operators, + and., provider that the following postulates are satisfied.

 

T1: Commutative Law

(a)A+B = B+A

(b)                        A B = BA

 

T2: Associative Law

(a) (A+B) +C = A+ (B+C)

 

(b) (A B) C = A (B C)

 

T3: Distributive Law

(a)  A (B +C) = A B + AC

(b) A + (B C) = (A +B) (A+C)

 

T4: Identity Law

(a)  A+A =A

(b) A A =A

 

T5: Negative Law

(a)  (A’) =A’

(b) (A’’) = A

 

T6: Redundant Law

(a)  A+AB=A

(b) A (A +B) =A

 

T7: Null Law

(a)0 + A = A

(b) 1 A = A

 

 

(c) 1 + A = 1

(d) 0 A = 0

 

T8: Double Negation Law

(a)  A’ +A=1

(b) A’ A=0

 

T9: Absorption Law

(a)  A+A’B =A+B

(b) A (A’ + B) =AB

 

T10: De Morgan's Theorem

(a)  (A+B)’ = A’ B’

 

(b) (AB)’ = A’+B’

 

Example 1:

 

Using theorems,

 

A + A’ B = A l + A’ B

 

= A (l + B) + A’B

 

=A + AB + A’B

 

=A + B (A + A’)

 

= A + B

 


Using Truth Table


 

1 Verification Of De Morgan's Theorems:

 

        De Morgan's First Theorem states:

 

The complement of a product of variables is equal to the sum of the complements of the individual variables

 

        De Morgan's Second Theorem states:

 

The complement of sum of variables is equal to the product of the complements of the dividable variables







 

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